Abstract
We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Δ4y
i
= λai+2yi+2, -1≤i≤n-2, y0 = Δ2y-1 = Δy
n
= Δ3yn-1 = 0, as the sequence 
varies. A comparison theorem of all eigenvalues is established for two sequences 
and 
with a
j
≥ b
j
, 1 ≤ j ≤ n, and the existence of positive eigenvector corresponding to the smallest eigenvalue of the problem is also obtained in this paper.
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Ji, J., Yang, B. Eigenvalue comparisons for boundary value problems of the discrete beam equation. Adv Differ Equ 2006, 081025 (2006). https://doi.org/10.1155/ADE/2006/81025
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DOI: https://doi.org/10.1155/ADE/2006/81025